Extracting the frequencies of the pinna spectral notches ... · Perceptual Interfaces and Reality...

Extracting the frequencies of the pinna spectral notches in

measured head related impulse responses

Vikas C. Raykara) and Ramani Duraiswamib)

Perceptual Interfaces and Reality Laboratory, Institute for Ad-

vanced Computer Studies, Department of Computer Science,

University of Maryland, College Park, MD 20742, USA

B. Yegnanarayanac)

Department of Computer Science and Engineering,

Indian Institute of Technology, Madras, Chennai-600036, Tamilnadu, India

Received:

Running title: Extracting frequencies of pinna spectral notches

Short title: Extracting pinna spectral notch frequencies

a) Electronic address:[email protected] ; URL: http://www.cs.umd.edu/˜vikasb) Electronic address:[email protected] ; URL: http://www.umiacs.umd.edu/˜ramanic) Electronic address: [email protected] ; URL: http://speech.cs.iitm.ernet.in/

˜yegna ; This work was performed when the author was visiting the University of Maryland, College Park.

Typeset by REVTEX 4 for JASA 1

Raykar et. al., JASA

ABSTRACT

The Head Related Impulse Response (HRIR) characterizes the auditory cues cre-

ated by scattering of sound off a person’s anatomy. The experimentally measured

HRIR depends on several factors such as reflections from body parts (torso, shoul-

der, and knees), head diffraction, and reflection/diffraction effects due to the pinna.

Structural models (Algaziet al., 2002; Brown and Duda, 1998) seek to establish

direct relationships between the features in the HRIR and the anatomy. While there

is evidence that particular features in the HRIR can be explained by anthropometry,

the creation of such models from experimental data is hampered by the fact that

the extraction of the features in the HRIR is not automatic. One of the prominent

features observed in the HRIR, and one that has been shown to be important for

elevation perception, are the deep spectral notches attributed to the pinna. In this

paper we propose a method to robustly extract the frequencies of the pinna spec-

tral notches from the measured HRIR, distinguishing them from other confounding

features. The method also extracts the resonances described by Shaw (1997). The

techniques are applied to the publicly available CIPIC HRIR database (Algaziet al.,

2001c). The extracted notch frequencies are related to the physical dimensions and

shape of the pinna.

PACS numbers: 43.66.Qp, 43.64.Ha, 43.66.Pn

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I. INTRODUCTION

Humans have an amazing ability to localize a sound source, i.e., determine the distance, eleva-

tion, and azimuth of the sound source relative to them (Blauert, 1996; Middlebrooks and Green,

1991). The mechanisms responsible for the localization ability of the human hearing system have

been fairly well understood though not completely. Interaural Time and Level Differences (ITD

and ILD) are known to provide primary cues for localization in the horizontal plane, i.e., azimuth

of the sound source (Blauert, 1996; Kuhn, 1977; Strutt, 1907; Wightman and Kistler, 1997). How-

ever these differences do not account for the ability to locate sound for positions in the so called

cone of confusion, which have the same ITD cues, or those with the same ILD cues (tori of con-

fusion (Shinn-Cunninghamet al., 2000)). This can be explained by the creation of distinctive

location specific features in the received sound arising due to interactions with the torso, head, and

pinna. This filtering process can be modeled using a complex frequency response function called

the Head Related Transfer Function (HRTF). For a particular sound source location, the HRTF is

defined as the ratio of the complex sound pressure level (SPL) at the eardrum to the SPL at the

location of the center of the head when the listener is absent. The corresponding impulse response

is called the Head Related Impulse Response (HRIR).

The HRTF varies significantly between different individuals due to differences in the sizes and

shapes of different anatomical parts like the pinnae, head, and torso. Applications in the creation of

virtual auditory displays require individual HRTFs for perceptual fidelity. A generic HRTF would

not work satisfactorily since it has been shown that non-individual HRTF results in poor elevation

perception (Wenzelet al., 1993). The usual customization method is the direct measurement of

HRTFs, which is a time consuming and laborious process. Other approaches that have met with

varying success include numerical modeling (Kahanaet al., 1999), frequency scaling the non-

individual HRTF to best fit the listeners one (Middlebrooks, 1999) and database matching (Zotkin

et al., 2002).

A promising approach for HRTF customization is based on building structural models (Algazi

et al., 2002; Brown and Duda, 1998; Raykaret al., 2003) for the HRTF. Different anatomical

parts contribute to different temporal and spectral features in the HRIR and HRTF respectively.

Structural models aim to study the relationship between the features and anthropometry. While

good geometrical models (Algaziet al., 2002; Duda and Martens, 1998) exist for the effects of

head, torso and shoulders, a simple model for the pinna that connects pinna anthropometry to the

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features in the HRIR does not exist.

The prominent features contributed by the pinna are the sharp notches in the spectrum, com-

monly called as thepinna spectral notches. There is substantial psychoacoustical (Mooreet al.,

1989; Wrightet al., 1974), behavioral (Gardner and Gardner, 1974; Hebrank and Wright, 1974a;

Hofmanet al., 1998), and neurophysiological (Poon and Brugge, 1993a,b; Tollin and Yin, 2003)

evidence to support the hypothesis that the pinna spectral notches are important cues for vertical

localization, i.e., determining the elevation of the source.

One difficulty in developing structural models for the pinna is that it is difficult to automatically

extract these frequencies from measured data. Once we have quantitative values for the frequen-

cies of the spectral peaks and notches, a model could be built relating them to the shape and the

anthropometry of the pinna. Based on these, new approaches for HRTF customization using these

features could be developed, and the role of the pinna in spatial localization better understood. Var-

ious psychoacoustical and neurophysiological experiments which explore the significance of the

pinna spectral notches can benefit from a procedure that automatically extracts the pinna spectral

notches from the measured impulse responses.

The focus of the work presented in this paper is to automatically extract the frequencies cor-

responding to the spectral notches. A major difficulty is that the experimentally measured HRIR

includes the combined effects of the head diffraction and shoulder, torso, and, as an artifact, the

knee reflection. Robust signal processing techniques need to be developed to extract the frequen-

cies of the spectral notches due to the pinna alone, in the presence of these confounding features.

The methods proposed are based on the residual of a linear prediction model, windowed autocor-

relation functions, group-delay function and all-pole modeling, guided by our prior knowledge of

the physics of the problem. Our methods also extracts the normal modes first described by Shaw

(1997).

Several studies were made to approximate the HRTFs by pole-zero models (Asanoet al., 1990;

Blommer and Wakefield, 1997; Durant and Wakefield, 2002; Hanedaet al., 1999; Kulkarni and

Colburn, 2004). These studies fit a pole-zero model based on a suitable error measure. However

since the spectral notches extracted by them are caused due to different phenomena it is not obvious

which of the spectral notches extracted by the model are due to the pinna.

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II. STRUCTURAL COMPOSITION OF THE HRIR

Following the work of Algaziet al. (2001b) we illustrate the potential of explaining and even-

tually synthesizing HRTFs from the anthropometry. To this end we will consider the measured

HRIRs from the CIPIC database (Algaziet al., 2001c). This is a public domain database of high

spatial resolution HRIR measurements along with the anthropometry for 45 different subjects. The

azimuth is sampled from−80o to 80o and the elevation from−45o to +231o in a head-centered

interaural polar coordinate system (Algaziet al., 2001c). For any given azimuth, we form a two

dimensional array, where each column is the HRIR or the HRTF for a given elevation, and the

entire array is displayed as an image. This method of visualization helps identify variation of dif-

ferent features with elevation (Algaziet al., 2001a). Fig. 1 shows the HRIR and HRTF images (for

all elevations) corresponding to azimuth00 for the right ear for subject 10 in the CIPIC database.

In Fig. 1 (a) the gray scale value represents the amplitude of HRIR, and in Fig. 1 (b) it is the mag-

nitude of the HRTF in dB. The different features corresponding to different structural components

are also marked by hand.

Composition of the responses in terms of head diffraction, head and torso reflection, pinna ef-

fects and the knee reflection artifact can be seen both in the time domain and in the frequency

domain. Most features marked in Fig. 1 were confirmed experimentally with the KEMAR man-

nequin, where the responses were measured by removing and adding different parts like the pinna,

head and torso (Algaziet al., 2001b).

Three distinct ridges, which are marked as1, 2 and3, can be seen in the HRIR image plot

(Fig. 1 (a)). The first distinct ridge is due to the direct sound wave that reaches the pinna. We see

that immediately after the direct wave, activity is seen in the close vicinity (within 1.2 ms), which

is due to diffraction of the sound around the head and the pinna. The corresponding diffraction

pattern due to the head in the frequency domain can be explained by Lord Rayleigh’s analytical

solution for scattering from a sphere (Duda and Martens, 1998; Strutt, 1907). The effect of head

diffraction is more prominent in the contralateral HRTF than in the ipsilateral HRTF .

The second valley shaped ridge between1 ms and2 ms is due to the reflected wave from the

torso, reaching the pinna. The delay between the direct and the reflected sound from the torso

is maximum above the head, and decreases on either side. This can be explained using simple

ellipsoidal models for the head and torso (Algaziet al., 2002). In the frequency domain the effect

of this delay is the arch shaped comb-filter notches that can be seen throughout the spectrum (see

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Fig. 1 (b)). Some studies have shown that the notches of the comb-filter in the low frequency

range (< 3 kHz) could be used as a potential cue for vertical localization for low frequency sounds

(Algazi et al., 2001a).

The activity seen after2 ms is due to knee reflections, since these measurements were done

with the subjects seated (Algaziet al., 2001c). This is confirmed by the observation that similar

activity is not seen in the back (ϕ > 90o) and absent in the KEMAR. The other artifact is the

faint pulse (marked 4 in Fig. 1(a)) seen arriving before the main pulse. This is probably due to

the nature of the probe microphone used in the measurements (Algaziet al., 2001c). The probe

microphone has a 76 mm silicone probe tube which conducts the acoustic wave to the microphone.

It is likely that the signal first hits the microphone outside before reaching the probe.

The other prominent features in the frequency domain, but difficult to see in the time domain,

are the prominent notches above5 kHz. Three prominent notches can be seen in Fig. 1(b) for

elevations from−45o to 90o. As the elevation increases the frequency of these notches increases.

Experiments with the KEMAR mannequin, in which the HRIRs were measured with and without

the pinna (Algaziet al., 2001b), confirm that these notches are caused due to the pinna. Also

present in the response are the resonances due to the pinna (the bright patches in the HRTF image

in Fig. 1 (b)). The resonances correspond to the six normal modes which were experimentally

measured by Shaw (1997) and numerically verified by Kahanaet al. (1999).

Batteau (1967) suggested that the structure of the pinna caused multiple reflections of sound,

and the delay between the direct and the reflected sound varies with the direction of the sound

source, providing a localization cue. These delays cause the notches in the spectrum. Hebrank and

Wright (1974a,b) attributed the pinna spectral notches to the reflection of sound from the posterior

concha wall. This idea was further refined by Lopez-Poveda and Meddis (1996) who incorporated

diffraction in the model.

Previous studies done both on humans and animals that discuss the pinna features can be clas-

sified as: psychoacoustical (Langendijk and Bronkhorst, 2002; Mooreet al., 1989; Wrightet al.,

1974), behavioral (Gardner and Gardner, 1974; Hebrank and Wright, 1974a; Hofmanet al., 1998)

and neurophysiological (Poon and Brugge, 1993a,b; Tollin and Yin, 2003). Psychoacoustical ex-

periments have demonstrated that high frequencies are necessary for localization in the vertical

plane (Gardner and Gardner, 1974; Hebrank and Wright, 1974b; Musicant and Butler, 1984). By

progressively occluding the pinna cavities, it was shown that localization ability decreases with in-

creasing occlusion (Gardner and Gardner, 1974). Hofmanet al. (1998) measured the localization

6


ability of four subjects before and after the shapes of their ears were changed by inserting plastic

moulds in the pinna cavity. Although localization of sound elevation was dramatically degraded

immediately after the modification, accurate performance was steadily acquired again.

The spectral peaks and the notches are the dominant cues contributed by the pinna. Since the

notch frequency varies smoothly with elevation, it is thought to be the main cue for perception

of elevation. On the other hand, the spectral peaks do not show this smooth trend. However,

it is likely that the presence or absence of the spectral peak could itself be a strong cue for the

elevation. For example, the second normal mode identified by Shaw is excited strongly only for

elevations around900. Wright et al. (1974) present experiments to determine whether delays

caused due to pinna reflections are detectable by humans. The results show that delay times of 20

µs are easily recognizable when the amplitude ratio of the delayed signal to the leading signal is

greater than 0.67. Just noticeable results agreed with the measurements of the minimum audible

angle for monaural localization. Experiments by Mooreet al. (1989) show that changes in the

center frequency of the notches are detectable even for rather narrow notches. Experiments on

cats suggest that single auditory nerve fibers are able to signal in their discharge rates the presence

of a spectral notch embedded in bursts of noise or in continuous noise (Poon and Brugge, 1993a).

A vertical illusion that was observed in cats by Tollin and Yin (2003) can be explained well by a

model that attributes vertical localization to recognition of the spectral shape cues.

Thus many studies have clearly established the importance of the pinna spectral notches in

the ability to localize sounds. However we must reiterate that these studies are not able to relate

the location of the notch to the pinna anthropometry, something that may be of importance in

applications that seek to create personalized HRTFs without the measurements.

While previous studies address the issue of how the HRTF iscomposed, there is no attempt to

decomposethe measured HRTF of a real subject into different components. Structural models aim

to decompose the HRIR into different components and then build a model for each component.

III. EXTRACTING THE FREQUENCIES OF PINNA SPECTRAL NOTCHES

One obvious way to extract the spectral notches and peaks is through pole-zero modeling

(Makhoul, 1975; Steiglitz and McBride, 1965). Several studies were made to approximate the

HRTFs by pole-zero models (Asanoet al., 1990; Blommer and Wakefield, 1997; Durant and

Wakefield, 2002; Hanedaet al., 1999; Kulkarni and Colburn, 2004). Figure 2 shows a typical

7


HRIR (subject 10, right ear, elevation45o and azimuth0o) we consider for illustration throughout

this section. The HRIR is 200 samples long at a sampling frequency of 44.1 kHz, corresponding

to 4.54 ms. The log magnitude spectrum, a(12, 12)th order pole-zero model spectrum and a12th

order all-pole model spectrum are also shown in the figure. As can be seen from the plots, due to

the combined effects of different phenomena, it is difficult to isolate the notches due to the pinna

alone. Also, in order to approximate the spectrum envelope better, the model would typically need

to be of high order (> 30). Even with the increased order, it is not guaranteed that the relevant

notches can be captured. Pole-zero or all-pole models merely approximate the spectrum envelope,

as best as they can, depending on the order of the model and the criterion used for approxima-

tion. Both the order and the criteria are independent of the nature of the signal being analyzed,

and also the features expected to be highlighted. Thus these modeling techniques are unlikely to

bring out the specific features one is looking for in the HRIR signal. Our proposed methods do not

rely on any models. We apply several signal processing techniques, including windowing, linear

prediction residual analysis, group-delay function and autocorrelation. We will motivate these in

the following discussions and present the complete algorithm at the end.

In the measured HRIR there is a very faint pulse arriving before the main direct pulse, due to

the nature of the measurement setup. This behavior is likely to cause problems in analysis and

hence we consider the signal from the instant of the main pulse (around 0.8 ms in Fig. 2(a) ). This

instant is found by taking the slope of the unwrapped phase spectrum or by locating the instant

of the maximum amplitude in the signal and shifting back till there is a increase in the signal

amplitude.

The spectral notches are caused due to multiple reflections from different parts like the head,

torso, knees, and pinna cavities. In order to highlight the effects due to pinna alone, the HRIR

signal is first windowed using a half Hann window (Oppenheim and Schafer, 1989). Windowing

in the time domain helps isolate the direct component of the signal from the reflected components.

A window of size 1.0 ms is used in order to eliminate the torso reflection (at around 1.6 ms

in Fig. 2(a)) and the knee reflection (at around 3.2 ms in Fig. 2(a)). Fig. 3(b) shows the log

magnitude spectrum of the windowed signal. We see that windowing the waveform reduces the

effect of reflection significantly compared to the log magnitude spectrum in Fig. 2(b). We would

like to point out that the exact size of the window is not crucial. A window size of 1.0 ms should

be sufficient to suppress the reflections due to the torso and the knees.

We extract the spectral notches from the group-delay function rather than the magnitude spec-

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trum. The additive nature of the phase spectra of systems in cascade and the high frequency

resolution properties of the group-delay functions help in providing better resolution of peaks and

valleys even for a short time segment of the data (Yegnanarayana, 1978). The group delay func-

tion is the negative of the derivative of the phase spectrum of a signal (Yegnanarayana, 1978;

Yegnanarayanaet al., 1984). IfX(ω) is the complex frequency response of a signalx(n), then the

group-delay functionτ(ω) is given by,

τ(ω) = −dθ(ω)

dω(1)

whereω is the angular frequency, andθ(ω) is the phase angle ofX(ω). The group-delay function

can be computed directly using the Fourier transform ofx(n) andnx(n), as follows (Oppenheim

and Schafer, 1989). LetX(ω) andY (ω) be the Fourier transforms ofx(n) andnx(n), respectively.

X(ω) =N−1∑n=0

x(n)e−jωn = XR(ω) + jXI(ω),

Y (ω) =N−1∑n=0

nx(n)e−jωn = YR(ω) + jYI(ω). (2)

Since

log X(ω) = log |X(ω)|+ jθ(ω), (3)

the group-delay function can be written as

τ(ω) = − d

dω[θ(ω)] = −Im(

d

dω[log X(ω)])

=XR(ω)YR(ω) + XI(ω)YI(ω)

X2R(ω) + X2

I (ω), (4)

whereIm(z) corresponds to the imaginary part ofz. Fig. 3(c) shows the group-delay function of

the windowed signal (window size 1.0 ms). Compared to the log magnitude spectrum in Fig. 3(b),

the group-delay function shows a better resolution of the notches.

However, windowing reduces the frequency domain resolution and also introduces artifacts.

The artifacts of windowing may also mask or alter the frequencies of the spectral notches due to

the pinna. One way to reduce the artifacts due to windowing is to remove the interdependence

among adjacent signal samples by using the Linear Prediction (LP) residual of the original HRIR

and then windowing the residual. This corresponds to removing the resonances from signal.

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The residual signal is derived using a12th order LP analysis (Makhoul, 1975). LP analysis

basically fits an all-pole model to the given signal. In LP analysis the signalx(n) is predicted

approximately from a linearly weighted summation of the pastp samples, i.e.,

x̂(n) = −p∑

k=1

akx(n− k). (5)

The error in the prediction, i.e., the LP residual is therefore given by,

e(n) = x(n)− x̂(n) = x(n) +

p∑

k=1

akx(n− k). (6)

The total squared error is

E =∑

n

e(n)2 =∑

n

[ x(n) +

p∑

k=1

akx(n− k) ]2. (7)

Minimization of the mean squared error with respect to the coefficients{ak} gives the following

normal equations (Makhoul, 1975)

p∑

k=1

akR(n− k) = −R(k), k = 0, 1, . . . , p, (8)

whereR(k) =∑

n x(n)x(n − k) is called the autocorrelation function for a lag ofk samples.

Eq. 8 can be solved to get the coefficients{ak}. Substituting the solution of the normal equations

Eq. 8 into the expression for the error in Eq. 6 gives the sequence corresponding to the minimum

total error, the LP residual.

LP analysis can be interpreted as the removal of redundancy in the signal samples by removing

the predictable part from the signal. The linearly weighted past samples are used to predict the

sample at the current sampling instant. The LP residual looks like noise, as correlation among

samples is significantly reduced compared to the original signal. The autocorrelation function of

the LP residual looks like an impulse at the origin (zero delay) with very small amplitudes for

other lags. Effect of direct windowing of the LP residual is shown in Fig. 4, where the spectral

notches can be seen to appear more prominently compared to the plots in Fig. 3.

The autocorrelation function of the windowed LP residual helps to reduce the effects due to

truncation and noise. The autocorrelation functionR(m) of a signalx(n) of lengthN is given by

R(m) =N−1∑n=m

x(n)x(n−m). (9)

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The autocorrelation function of a signal produces decreasing amplitudes away from its peak,

which helps in computing the group-delay function better, while at the same time preserving most

of the details of the spectral envelope. The resolution of the spectral components is enhanced in

the group-delay function of the autocorrelation function of the windowed LP residual. Using the

zero threshold for the group delay function, all valleys below the zero value are marked as relevant

notches and their frequencies are noted. In practice a slightly lower threshold of -1 was found to

give better results and eliminated any spurious nulls caused due to windowing.

The sequence of signal processing operations is summarized below and the effect of each step

on the HRIR and HRTF is shown in Fig. 5.

1. Determine the initial onset of the HRIR and use the HRIR from that instant.

2. Derive thepth (p = 10 to 12) order LP residual from the given HRIR (Fig. 5(b)).

3. Window the LP residual using a half Hann window of around 1.0 ms (Fig. 5(c)).

4. Compute the autocorrelation function of the windowed LP residual (Fig. 5(d)).

5. Window the autocorrelation function using a half Hann window of around 1.0 ms (Fig. 5(e)).

6. Compute the group-delay function of the windowed autocorrelation function (Fig. 5(k)).

7. Threshold the group-delay function and locate the local minima.

Since the spectra of the windowed LP residual is a smooth function with nulls, the spectrum can

be inverted to obtain a spectrum with prominent peaks. An all-pole model can be fit to this spec-

trum by computing the autocorrelation function, and then applying the Levinson-Durbin method

(Makhoul, 1975) for the first few (10) autocorrelation coefficients. The frequencies corresponding

to the complex roots of the all-pole model correspond to the frequencies of the prominent nulls in

the spectrum of the windowed HRIR. This method also helps to get the depth and the width of the

spectral notches. However, in order to extract the frequencies of the spectral notches the method

based on group-delay is preferred since we do not need to specify the model order.

IV. RESULTS

The developed algorithm is applied on the measured HRIRs of different subjects and for dif-

ferent elevations and azimuth angles in the CIPIC database. As an example, Figures 6(a)-(h) show

the spectral notch frequencies for the right ear HRTF corresponding to subject 10 in the CIPIC

database. The notch frequencies are plotted as a function of elevation for different azimuths. Note

11


that negative azimuth angles correspond to the contralateral HRTF, with the pinna in the shadow

region of the head and the diffraction effects prominent. However, some pinna notches are still

dominant and we were able to extract them using the same algorithm. A few notches due to head

diffraction effects also appear (see Fig. 6(h)).

The pinna notches in the contralateral side can be explained if we assume that the sound

diffracts around the head entering the contralateral concha at approximately the same elevation

angle as if the source were in the ipsilateral hemisphere (Lopez-Poveda and Meddis, 1996). How-

ever, since elevation perception is essentially thought to be monaural (Middlebrooks and Green,

1991) it is likely that humans use only the near ear (i.e. the ear closest to the source) for vertical

localization. It is still possible that the pinna notches in the contralateral HRTF could provide extra

cues for vertical localization. Fig. 6 (i) shows the notch frequencies for the left pinna for subject

10 and azimuth0o. It was observed for most subjects that left and the right pinna do not have

the same shape and dimensions (Algaziet al., 2001c). The frequencies of the notches and their

variation with elevation are different for the left and the right pinna. Fig. 7 (a)-(i) shows the same

results for 9 different subjects and for azimuth0o. Similar results are obtained when the analysis

is applied all the subjects in the database.

We note that LP analysis can also be used to extract spectral peaks in the spectrum. The poles

extracted by LP analysis appear to correspond to the resonances of the pinna reported by Shaw

(1997), who identified the normal modes by searching for the response maxima as the sound

frequency and the source position were varied. The first mode is a simple quarter-wavelength

depth resonance with uniform sound pressure across the base of the concha. It is strongly excited

from all directions. The other modes are essentially transverse and fall into two groups: a vertical

pair(modes 2 and 3) and a horizontal triplet (modes 4, 5 and 6). The poles extracted by LP

analysis correspond to the resonances of the pinna reported by Shaw. Fig. 8 shows the frequency

response of the12th order all-pole model for the subject10 for azimuth0o as a function of different

elevations as a mesh plot. These six modes are marked in the plot.

V. SPECTRAL NOTCHES AND PINNA SHAPE

The proposed procedure was successful in extracting the pinna spectral notches, visible to

the human eye. We hope this would be a useful tool for researchers to study the significance

of the pinna spectral notches to location perception and also to build structural models for the

12


pinna. While perceptual tests are beyond the scope of this paper, we demonstrate a potential use

of our procedure by showing that the pinna spectral notches are indeed related to the shape and

anthropometry of the pinna.

The structure of the pinna is fairly complicated and difficult to characterize by simple models.

To a first approximation the response can be characterized by peaks and notches observed in the

spectrum. Fig. 9 shows the simple reflection model. The direct wave incident at an angleϕ is

reflected from the concha wall. Ifx(t) is the incident wave then the measured signaly(t) is the

sum of the direct and the reflected wave.

y(t) = x(t) + ax(t− td(ϕ)), (10)

wherea is the reflection coefficient andtd(ϕ) is the time delay given by

td(ϕ) =2d(ϕ)

c, (11)

where2d(ϕ) is the distance corresponding to the delay andc is the speed of the sound (approxi-

mately343 m/sec). The distanced(ϕ) depends on the angleϕ and shape of the pinna. The delay

td(ϕ) causes periodic notches in the spectrum, whose frequencies are given by

fn(ϕ) =(2n + 1)

2td(ϕ)=

c(2n + 1)

4d(ϕ), n = 0, 1, . . . (12)

The frequency of the first spectral notch is given by,

f0(ϕ) =c

4d(ϕ)(13)

In practice there are multiple reflections occurring in the pinna. Each reflection gives rise to

a series of periodic spectral notches. In the previous section we extracted the frequencies of the

spectral notches. From Equation 13 we can calculate the distanced(φ) corresponding to the notch

frequencyf0(φ). As the angleφ is varied, the notch frequency varies depending on the the shape of

the pinna. The variation of the notch frequency reflects the shape of the pinna. The pinna images

as well as the ear anthropometry are available in CIPIC database. The distance can be marked

on the pinna image approximately. Fig. 10(a) shows the notch frequencies extracted for azimuth

0o and elevation varying from−45o to 900 (subject 10 right pinna). We consider only elevations

in front of the head, since for elevations behind the ear the mechanism of the spectral notches is

not clear. For each of the extracted notches the corresponding distance is plotted on the image of

the pinna (Fig. 10(e)) and appears consistent with this argument. It is interesting to see that the

13


shape and dimensions of the concha are clearly seen in the extracted frequencies of the spectral

nulls. The first spectral null thus appears to be caused due to reflection from the concha. As the

elevation is varied it traces out the shape of the concha. The third spectral null could be due to the

inner cavity in the concha caused by the crus helias dividing the concha into two. Fig. 10 shows

the same results for three other subjects in the CIPIC database, and exhibit similar trends.

These results suggest that the shape of the different cavities in the pinna are as important as

the gross dimensions. A model for the pinna should take this into consideration. Since measure-

ment of the HRIR is a tedious process, a particulary appealing method for synthesizing the HRIR

would be to take the image of an pinna and obtain the notch frequencies by analyzing the pinna

anthropometry.

VI. SUMMARY

We proposed signal processing algorithms for extraction of the pinna spectral notch frequencies

from experimentally measured HRIRs. The difficulties in the analysis of HRIR due to combined

effects of several components are discussed, and windowing in the time domain was proposed to

reduce the effects of the reflected components. The effectiveness of the methods in isolating and

determining the frequencies of the spectral nulls due to pinna has been demonstrated using the

CIPIC database. The extracted spectral notch frequencies are related to the shape of the pinna.

The code is made available to the research community on the first author’s website.

VII. ACKNOWLEDGEMENTS

The support of NSF award ITR-0086075 is gratefully acknowledged. We would also like to

thank associate editor and the two reviewers for their comments and suggestions which helped to

improve the clarity and quality of the paper.

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17


LIST OF FIGURES

1 a) HRIR and (b) HRTF displayed as images for the right ear for subject 10 in the

CIPIC database for azimuth angleθ = 0o for all elevations varying from−45o to

+230.625o. The different features are marked in both the HRIR and the HRTF

plots. In (a) the gray scale value represents the amplitude of HRIR, and in (b) the

gray scale value is the log magnitude of the HRTF in dB. . . . . . . . . . . . 20

2 (a) A typical HRIR for an elevation of45o and an azimuth of0o, (b) the log mag-

nitude spectrum, a(12, 12)th order pole-zero model spectrum and a12th order all-

pole model spectrum. In the plots the all-pole spectrum and the pole-zero spectrum

are displaced vertically by 5 dB and 10 dB, respectively, for clarity. . . . . . . . 21

3 Effect of windowing the HRIR. (a) HRIR (solid line) and half-Hann window (dot-

ted line) of size 1.0 ms, (b) log magnitude spectra of the windowed signal, and (c)

the corresponding group-delay function. . . . . . . . . . . . . . . . . . . . 22

4 Effect of windowing the LP residual of the HRIR. (a) The12th order LP resid-

ual and half Hann window of size 1.0 ms, (b) the log magnitude spectra of the

windowed LP residual signal and, (c) the corresponding group-delay function. . . 23

5 Signal processing steps for extracting the pinna null frequencies. (a) Original

HRIR signal, (b)12th order LP residual, (c) windowed LP residual (1.0 ms half

Hann window), (d) autocorrelation function of the windowed LP residual and (e)

windowed autocorrelation function (0.7 ms half Hann window). The plots (f), (g),

(h), (i) and (j) show the log magnitude spectrum (in dB) corresponding to signals in

(a), (b), (c), (d) and (e), respectively. The plot (k) shows the group-delay function

of the windowed autocorrelation function. The local minima in the group-delay

function (zero thresholded) are shown. . . . . . . . . . . . . . . . . . . . . 24

6 The spectral notch frequencies extracted for subject 10right pinna in the CIPIC

database for azimuth angles (a)0o, (b)15o, (c)45o, (d)65o, (e)80o, (f)−15o, (g)−45o

and (h)−65o. (i) The spectral notch frequencies corresponding to theleft pinna of

subject 10 for azimuth0o. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7 The spectral notch frequencies for different elevations extracted for the right pinna

for azimuth0o for different subjects in the CIPIC database. . . . . . . . . . . . 26

18


8 Frequency response of the12th order all pole model for azimuth0o as a function

of different elevations. The six modes are approximately marked. . . . . . . . . 27

9 A simple reflection model for the pinna spectral notches. The direct wave incident

at an angleφ gets reflected from the concha. The time delay corresponds to a

length of2d. The pinna image is taken from the CIPIC database. . . . . . . . . 28

10 The spectral notch frequencies for different elevations (from−45o to 90o) ex-

tracted for the right pinna for azimuth0o (a) subject 10, (b) subject 27, (c) subject

134 and (d) subject 165 in the CIPIC database. The dimensions corresponding

to the spectral notches marked on the pinna image for (e) subject 10, (f) subject

27, (g) subject 134, and, (h) subject 165 respectively. The pinna images are taken

from the CIPIC database. . . . . . . . . . . . . . . . . . . . . . . . . . . 29

19


Tim

e(m

s)

Elevation(deg)0 50 100 150 200

0

1

2

3

4

Elevation(deg)

Fre

quen

cy(k

Hz)

0 50 100 150 200

0

5

10

15

20−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

−100

−80

−60

−40

−20

0

(a) (b)

Pinna Nulls

Pinna resonances Torso reflection

Knee reflection Head diffraction+Pinna effects

1

2

3

Faint initial pulse

4

FIG. 1. a) HRIR and (b) HRTF displayed as images for the right ear for subject 10 in the CIPIC database

for azimuth angleθ = 0o for all elevations varying from−45o to +230.625o. The different features are

marked in both the HRIR and the HRTF plots. In (a) the gray scale value represents the amplitude of HRIR,

and in (b) the gray scale value is the log magnitude of the HRTF in dB.

20


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

−0.5

0

0.5

Time (ms)

(a)

Am

plitu

de

0 5 10 15 20−40

−20

0

20

40

Frequency (kHz)

Log

mag

nitu

de (d

B)

(b)

OriginalAll−pole modelPole−zero model

FIG. 2. (a) A typical HRIR for an elevation of45o and an azimuth of0o, (b) the log magnitude spectrum,

a (12, 12)th order pole-zero model spectrum and a12th order all-pole model spectrum. In the plots the

all-pole spectrum and the pole-zero spectrum are displaced vertically by 5 dB and 10 dB, respectively, for

clarity.

21


0 1 2 3−0.5

0

0.5

1

(a)

Time (ms)

Ampli

tude

0 10 20

−40

−20

0

20

40

Log m

agnit

ude (

dB)

(b)

Frequency (kHz)0 10 20

−100

−50

0

50

Grou

p dela

y

Frequency (kHz)

(c)

FIG. 3. Effect of windowing the HRIR. (a) HRIR (solid line) and half-Hann window (dotted line) of size

1.0 ms, (b) log magnitude spectra of the windowed signal, and (c) the corresponding group-delay function.

22


0 1 2 3−1

0

1

Time (ms)

(a)Am

plitu

de

0 10 20−30

−20

−10

0

Frequency (kHz)

Log

mag

nitu

de (d

B)

(b)

0 10 20−50

0

50

Frequency (kHz)

(c)

Gro

up d

elay

FIG. 4. Effect of windowing the LP residual of the HRIR. (a) The12th order LP residual and half Hann

window of size 1.0 ms, (b) the log magnitude spectra of the windowed LP residual signal and, (c) the

corresponding group-delay function.

23


−0.5

0

0.5(a

)

−0.2

0

0.2

(b)

−0.2

0

0.2

(c)

−0.2

0

0.2

(d)

0 1 2 3−0.2

0

0.2

Time (ms)

(e)

−50

0

50

(f)

−40

−20

0

(g)

−40

−20

0

(h)

−40

−20

0

(i)

−30

−20

−10

0

(j)0 5 10 15 20

−6−4−2

02

Frequency (kHz)(k

)

Log

Mag

nitud

e (d

B)

Ampli

tude

FIG. 5. Signal processing steps for extracting the pinna null frequencies. (a) Original HRIR signal, (b)

12th order LP residual, (c) windowed LP residual (1.0 ms half Hann window), (d) autocorrelation function

of the windowed LP residual and (e) windowed autocorrelation function (0.7 ms half Hann window). The

plots (f), (g), (h), (i) and (j) show the log magnitude spectrum (in dB) corresponding to signals in (a), (b),

(c), (d) and (e), respectively. The plot (k) shows the group-delay function of the windowed autocorrelation

function. The local minima in the group-delay function (zero thresholded) are shown.

24


Elevation (degrees)

Fre

qu

en

cy (

kHz)

Subject 10 right pinna azimuth 0.00o

0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

10

(a)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

10

(b)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18 −80

−70

−60

−50

−40

−30

−20

−10

0

10

(c)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18−70

−60

−50

−40

−30

−20

−10

0

10

(d)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18 −70

−60

−50

−40

−30

−20

−10

0

10

(e)

Elevation (degrees)F

req

ue

ncy

(kH

z)

Subject 10 right pinna azimuth −15.00o

0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

(f)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

(g)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18−80

−70

−60

−50

−40

−30

−20

−10

0

(h)

Elevation (degrees)

Fre

qu

en

cy (

kHz)

Subject 10 left pinna azimuth 0.00o

0 50 100 150 200

0

2

4

6

8

10

12

14

16

18−60

−50

−40

−30

−20

−10

0

10

(i)

FIG. 6. The spectral notch frequencies extracted for subject 10right pinna in the CIPIC database for

azimuth angles (a)0o, (b)15o, (c)45o, (d)65o, (e)80o, (f)−15o, (g)−45o and (h)−65o. (i) The spectral notch

frequencies corresponding to theleft pinna of subject 10 for azimuth0o.

25


Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

(a)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−60

−50

−40

−30

−20

−10

0

(b)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18−45

−40

−35

−30

−25

−20

−15

−10

−5

0

5

(c)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−50

−40

−30

−20

−10

0

(d)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−60

−50

−40

−30

−20

−10

0

10

(e)

Elevation (degrees)F

req

ue

ncy

(kH

z)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−60

−50

−40

−30

−20

−10

0

(f)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−50

−40

−30

−20

−10

0

(g)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−60

−50

−40

−30

−20

−10

0

(h)

Elevation (degrees)

Fre

qu

en

cy (

kHz)


0 50 100 150 200

0

2

4

6

8

10

12

14

16

18

−60

−50

−40

−30

−20

−10

0

10

(i)

FIG. 7. The spectral notch frequencies for different elevations extracted for the right pinna for azimuth0o

for different subjects in the CIPIC database.

26


FIG. 8. Frequency response of the12th order all pole model for azimuth0o as a function of different

elevations. The six modes are approximately marked.

27


Direct Wave

Reflected Wave

d

Concha

φ

crus helias

FIG. 9. A simple reflection model for the pinna spectral notches. The direct wave incident at an angleφ

gets reflected from the concha. The time delay corresponds to a length of2d. The pinna image is taken

from the CIPIC database.

28


Elevation (degrees)

Fre

qu

en

cy (

kH

z)


−40 −20 0 20 40 60 80

0

2

4

6

8

10

12

14

16

18

−70

−60

−50

−40

−30

−20

−10

0

10

(a)

Elevation (degrees)

Fre

qu

en

cy (

kH

z)


−40 −20 0 20 40 60 80

0

2

4

6

8

10

12

14

16

18

−50

−40

−30

−20

−10

0

10

(b)

Elevation (degrees)

Fre

qu

en

cy (

kH

z)


−40 −20 0 20 40 60 80

0

2

4

6

8

10

12

14

16

18 −45

−40

−35

−30

−25

−20

−15

−10

−5

0

5

(c)

Elevation (degrees)

Fre

qu

en

cy (

kH

z)


−40 −20 0 20 40 60 80

0

2

4

6

8

10

12

14

16

18

−40

−35

−30

−25

−20

−15

−10

−5

0

5

(d)

(e) (f) (g) (h)

FIG. 10. The spectral notch frequencies for different elevations (from−45o to 90o) extracted for the right

pinna for azimuth0o (a) subject 10, (b) subject 27, (c) subject 134 and (d) subject 165 in the CIPIC database.

The dimensions corresponding to the spectral notches marked on the pinna image for (e) subject 10, (f)

subject 27, (g) subject 134, and, (h) subject 165 respectively. The pinna images are taken from the CIPIC

database.

29

Extracting the frequencies of the pinna spectral notches ... · Perceptual Interfaces and Reality...

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